S-factor

In nuclear physics, the astrophysical S-factor S(E) is a rescaling of a nuclear reaction's total cross section σ(E) to account for the Coulomb repulsion between the charged reactants. It determines the rates of nuclear fusion reactions that occur in the cores of stars.

Definition

The quantity is defined as

$S(E)\equiv \frac{E}{\exp (-2\pi \eta )}\sigma (E)$,

where E is the energy, σ is the cross section, η is the dimensionless Sommerfeld parameter:

$\eta \equiv \frac{Z_1{Z}_2{e}^2}{4\pi {ϵ}_0\hslash v}$,

Z₁ Z₂ e² is the product of the charges of the reactants, ${ϵ}_0$ is the permittivity of free space, $\hslash$ is the reduced Planck constant and v is the relative incident velocity.

Motivation

See also: Gamow factor

The Coulomb barrier causes the cross section to have a strong exponential dependence on the center-of-mass energy E. The S-factor remedies this by factoring out the Coulomb component of the cross section.